[R-meta] formula for calculating variance

[Sicong Liu]

Dear All,

Hope all of you are doing well.

I have a question regarding the calculation of the effect size variance on OddsRatio metric and wish to hear your thoughts:

When computing the effect size variance based on odds ratio using binary data (assuming the four cells has observation number A, B, C, D like the example in Chapter 5 of Borenstein et al. (2009) book, p. 33), the formula suggested for calculating effect size variance is: var = 1/A + 1/B + 1/C + 1/D. My question is that if I convert the effect size from logOddsRatio to d, is it appropriate to calculate the effect size variance using the converted d in that: var = (n1 + n2)/(n1*n2) + d^2/(2*n1 + 2*n2) (Chapter 4, p. 27)? Regardless of the appropriateness, could you please explain the main differences between these two approaches in calculating effect size variances and how the selection between them may affect the modeling? 

Thank you very much and stay warm!

Cheers, 
Sicong
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